{"paper":{"title":"Analytical Approach to Parallel Repetition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"David Steurer, Irit Dinur","submitted_at":"2013-05-09T00:22:17Z","abstract_excerpt":"We propose an analytical framework for studying parallel repetition, a basic product operation for one-round two-player games. In this framework, we consider a relaxation of the value of a game, $\\mathrm{val}_+$, and prove that for projection games, it is both multiplicative (under parallel repetition) and a good approximation for the true value.\n  These two properties imply a parallel repetition bound as $$ \\mathrm{val}(G^{\\otimes k}) \\approx \\mathrm{val}_+(G^{\\otimes k}) = \\mathrm{val}_+(G)^{k} \\approx \\mathrm{val}(G)^{k}. $$\n  Using this framework, we can also give a short proof for the NP-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1979","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}